That should be a pretty decent shave soap as long as the coconut oil (cocos nucifera oil) percentage is not too high and it does not seem like it is since you have tested it.I think you are spot on with this. My (recent) favorite artisan soap/croap/cream (everyone’s definition is different) is Officina Artigiana Milano. It lathers easily and create a very rich cream which lasts for a long time. I find it superior to other soaps which are in similar price range or even more expensive. They do use most of the products you mention, although I can imagine it is not a perfect base and they can be criticized as well.
Here’s the ingredient list they use:
Aqua (Water), Stearic Acid, Cocos Nucifera Oil, Castor Oil, Prunus Amygdalus Dulcis (Sweet Almond) Oil, Argania Spinosa (Argan) Kernel Oil, Potassium Hydroxide, Parfum (Fragrance), Simmondsia Chinensis (Jojoba) Oil, Vitis Vinifera Seed Oil , sodium hydroxide, linalool
soap/croap/cream are kind of an ambiguous terms. The soap you have is what they call a dual lye soap. This is the most common for shave soaps. It uses both potassium hydroxide and sodium hydroxide lyes. The ratio between these two have a large impart on how hard/soft the soap will be. The more potassium hydroxide you have the harder the soap and vice versa. Correspondingly the harder the soap the longer it will take to load your brush. Also, a longer lasting soap will be harder. When a shaving soap crosses from a soap to a croap to a cream . Very subjective I would say.
Most bath bars are just made with potassium hydroxide, because you want a hard bar of soap that last a while.